Data Sufficiency

BTGmoderatorLU wrote: ↑

Mon Aug 03, 2020 7:28 am

Source: Princeton Review

The greatest number of a set of 4 numbers is 70. What is the average (arithmetic mean) of the set?

1) The median of the set is 25
2) The range of the set is 70

The OA is C

Let's take each statement one by one.

1) The median of the set is 25.

Since there are 4 numbers, the median would be the average of the 2nd and the 3rd number when the numbers are arranged in the ascending order. Since we do not know the value of the smallest number, we can't get the answer. Insufficient.

2) The range of the set is 70.

=> the smallest number = 0. However, since we do not know the values of the middle two numbers, we can't get the answer. Insufficient.

(1) and (2) together

Say the middle two numbers are x and y such that x ≤ y. Thus, the numbers arranged in the ascending order are

0, x , y, 70.

From statement (2), we have (x + y)/2 = 25 => y = 50 – x.

Again, the numbers are 0, x, (50 – x), 70.

Thus, average = [0 + x + (50 – x) + 70]/4 = 30. Sufficient.

Correct answer: [spoiler][/spoiler]

Hope this helps!

-Jay
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